A Space-Time Information Paradox by Anton Lorenz Vrba

Anton,

No, you needn't say more. Don't you want to know, though, when your algebra is wrong?

Wikipedia is not a great source for this kind of thing. However, (hopefully) fixing your link , one will find that "The Schwarzschild metric is a solution of Einstein's field equations in empty space, meaning that it is valid only outside the gravitating body. That is, for a spherical body of radius R the solution is valid for r > R. To describe the gravitational field both inside and outside the gravitating body the Schwarzschild solution must be matched with some suitable interior solution at r = R."

As I said.

Tom

Anton,

I'm planning to get back to you -- to discuss information and interactions -- as soon as I get my essay done.

This short note is to say: Many thanks for sharing your formatting system; it's as good as I've seen. For now, though, I've decided to plug on with my current system -- having little time for new tricks until I get my essay up.

However, as a return favour, I'm pleased for you to be the first to know publicly: "The quantum is classical." Me having the impression that such a conclusion might be close to your own thinking.

So, with the title settled -- "Deep physics, easy maths: The quantum is classical." -- the rest is downhill. (My use of that last reflecting some of the clever words you've invented!)

More soon, and my thanks again,

Gordon

Anton

Congratulations on a well-explained, ingenious and relevant essay on the contest Question. Its compactness is welcome because it allows one to concentrate on the few points to be understood.

Your approach is interesting, and if there is anywhere the paradox can be resolved it may be in pinpointing the slippery concept of "information". For example I strongly disagree with the prevailing point-photon particle concept. Will your arguments still stand if - for example - information is embedded in amplitude modulated continuous electromagnetic waves? What about if there is a discrete ether medium?

A friend read your essay but did not wish to join the online discussions directly, and emailed me the following comment:

"Special relativity has always been challenged by paradoxes, the twin paradox and the barn and ladder are the classics and well known. Vrba's information paradox is new to me, analysing the MM-experiment using a continues wave and Doppler shifts instead of a point particle does make sense and is closer to what happens in nature, his logic seems to be correct and I presume he has checked his maths - this is going to be interesting what explanation will be given"

With best wishes in the contest,

Vladimir

Dear Sir,

Your conclusion is very interesting. The following observations may interest you.

Transverse waves are always characterized by particle motion being perpendicular to the wave motion. This implies the existence of a medium through which the reference wave travels and with respect to which the transverse wave travels in a perpendicular direction. In the absence of the reference wave, which is a longitudinal wave, the transverse wave can not be characterized as such. All transverse waves are background invariant by its very definition. Since light is propagated in transverse waves, Maxwell used a transverse wave and aether fluid model for his equations. Feynman has shown that Lorentz transformation and invariance of speed of light follows from Maxwell's equations. Einstein's causal analysis in SR is based on Lorentz's motional theory where a propagation medium is essential to solve the wave equation. Einstein's ether-less relativity is not supported by Maxwell's Equations nor the Lorentz Transformations, both of which are medium (aether) based. Thus, the non-observance of aether drag (as observed in Michelson-Morley experiments) cannot serve to ultimately disprove the aether model. The equations describing space-time, based on Einstein's theories of relativity, are mathematically identical to the equations describing ordinary fluid and solid systems. Yet, it is paradoxical that physicists have denied aether model while using the formalism derived from it. They don't realize that Maxwell used transverse wave model, whereas aether drag considers longitudinal waves. Thus, the notion that Einstein's work is based on "aether-less model" is a myth. All along he used the aether model, while claiming the very opposite.

Regarding Einstein, there is a great degree of misinformation. The concept of measurement has undergone a big change over the last century leading to changes in "mathematics of physics". It all began with the problem of measuring the length of a moving rod. Two possibilities of measurement suggested by Mr. Einstein in his 1905 paper were:

(a) "The observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod, in just the same way as if all three were at rest", or

(b) "By means of stationary clocks set up in the stationary system and synchronizing with a clock in the moving frame, the observer ascertains at what points of the stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is the length of the rod"

The method described at (b) is misleading. We can do this only by setting up a measuring device to record the emissions from both ends of the rod at the designated time, (which is the same as taking a photograph of the moving rod) and then measure the distance between the two points on the recording device in units of velocity of light or any other unit. But the picture will not give a correct reading due to two reasons:

• If the length of the rod is small or velocity is small, then length contraction will not be perceptible according to the formula given by Einstein.

• If the length of the rod is big or velocity is comparable to that of light, then light from different points of the rod will take different times to reach the recording device and the picture we get will be distorted due to different Doppler shift. Thus, there is only one way of measuring the length of the rod as in (a).

Here also we are reminded of an anecdote relating to a famous scientist, who once directed two of his students to precisely measure the wave-length of sodium light. Both students returned with different results - one resembling the normally accepted value and the other a different value. Upon enquiry, the other student replied that he had also come up with the same result as the accepted value, but since everything including the Earth and the scale on it is moving, for precision measurement he applied length contraction to the scale treating the star Betelgeuse as a reference point. This changed the result. The scientist told him to treat the scale and the object to be measured as moving with the same velocity and recalculate the wave-length of light again without any reference to Betelgeuse. After sometime, both the students returned to tell that the wave-length of sodium light is infinite. To a surprised scientist, they explained that since the scale is moving with light, its length would shrink to zero. Hence it will require an infinite number of scales to measure the wave-length of sodium light!

Some scientists we have come across try to overcome this difficulty by pointing out that length contraction occurs only in the direction of motion. They claim that if we hold the rod in a transverse direction to the direction of motion, then there will be no length contraction. But we fail to understand how the length can be measured by holding the rod in a transverse direction. If the light path is also transverse to the direction of motion, then the terms c+v and c-v vanish from the equation making the entire theory redundant. If the observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod while moving with it, he will not find any difference because the length contraction, if real, will be in the same proportion for both.

The fallacy in the above description is that if one treats "as if all three were at rest", one cannot measure velocity or momentum, as the object will be relatively as rest, which means zero relative velocity. Either Mr. Einstein missed this point or he was clever enough to camouflage this, when, in his 1905 paper, he said: "Now to the origin of one of the two systems (k) let a constant velocity v be imparted in the direction of the increasing x of the other stationary system (K), and let this velocity be communicated to the axes of the co-ordinates, the relevant measuring-rod, and the clocks". But is this the velocity of k as measured from k, or is it the velocity as measured from K? This question is extremely crucial. K and k each have their own clocks and measuring rods, which are not treated as equivalent by Mr. Einstein. Therefore, according to his theory, the velocity will be measured by each differently. In fact, they will measure the velocity of k differently. But Mr. Einstein does not assign the velocity specifically to either system. Everyone missed it and all are misled. His spinning disk example in GR also falls for the same reason.

Einstein uses a privileged frame of reference to define synchronization and then denies the existence of any privileged frame of reference. We quote from his 1905 paper on the definition of synchronization: "Let a ray of light start at the "A time" tA from A towards B, let it at the "B time" tB be reflected at B in the direction of A, and arrive again at A at the "A time" t'A. In accordance with definition the two clocks synchronize if: tB - tA = t'A - tB."

"We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:--

1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.

2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other."

The concept of relativity is valid only between two objects. Introduction of a third object brings in the concept of privileged frame of reference and all equations of relativity fall. Yet, Mr. Einstein precisely does the same while claiming the very opposite. In the above description, the clock at A is treated as a privileged frame of reference for proving synchronization of the clocks at B and C. Yet, he claims it is relative!

Regards,

basudeba

Anton,

I agree, that information is a sort of a preserved quantity. But I do not agree, that information causes a change of any physical state. Information by itself cannot change anything real.

According to C.F.v.Weizsäcker information is nothing else than the a quantitative measure of FORM (in_form) that can be found on a physical structure or state. The more complex the structure or state is, the more information is needed to describe it.

By generalizing this relationship between fundamental physics and information theory von Weizsäcker concluded:

ENERGY is INFORMATION.

(in: Unity of Nature)

If we take this statement as a fundamental "relation" not only energy has to be conserved, Information has to be conserved as well. That means, no information can be, in principle, destroyed. The black hole information paradox is therefore no paradox, it is mehrely the result of an insufficient description of spacetime-singularities. No information is really destroyed by them. An actual information has only been transformed into a virtual information, that is stored in the underlying field.

To highlight this insufficience it is useful to remember the behavior of waves. We know that waves - if are out of phase - can cause complete destructive interference, which looks very like a violation of conservation of energy. But we know that every time light cancels light "at one location" there is another location - usually nearby - where light reinforces light, and all the energy that is missing from the canceled location shows up at the reinforced location.

I think, we have to reason about the black hole destruction of information in a very similar way. And here I agree with you again. Using information theory the black hole paradox can possibly be solved.

Anton,

Short and sweet is not problem at all when so accurately 'to the point'!

I think I have a simple logical solution for you, if you haven't already found it, but perhaps you can tell me on reading my essay.

Your axiom 3 stood out to me as nonsense before I'd finished reading it, so I was very pleased to discover that you'd found that too! There is however a slight 're-interpretation' of it that which works. It shows Einstein was closer than most think, but that one wrong assumption made nonsense of it all. It's actually better described in a Hadronic Journal paper here; Emission/SR/QM resolution (Unfortunately few read that).

But well done with the essay. Sometimes small is very beautiful.

Best of luck,

Peter

Dear Anton

The opening of your very good, but the conclusion was that to do I actually disappointment. It looks like you used a new question - answer more difficult - to answer the question posed.

http://fqxi.org/community/forum/topic/1802

Dear Anton; It seems you're still waiting for the reply that says, "Anton that's a lot of BS you published there, because of so and so."

Leaving the final nails to you, please consider:

In Fig. 1 you have L = AB = AC. So let's take the simple case where B and C are stationary in the same reference frame and A now moves away from both with speed v.

Clearly, if Alice sends duplicate signals to Bob and Charlie, they now receive the same information.

Let Alice now cut costs (eliminating duplication) and let Bob relay the message to Charlie via a mirror. Under you assumptions, Bob and Charlie still receive the same information.

Now let Bob install his shutter. Charlie now certainly receives less information than Bob and the paradox in your title is (in this simple case) a fallacy.

PS: Similar clarification of your gedanken yields the same result.

With best regards, please return the favour via my Essay. Thanks; Gordon

OK. In that case it would be very helpful to have one Figure showing the three key phases of your experiment:

(i) The initial position of the key equipment and personnel with their interrelationships.

(ii) An intermediate phase with Bob reflecting information to Charlie.

(iii) A later stage with Bob's shutter in place.

All the best; Gordon

Hello Anton,

Nice concise essay. I read over the paradox several times - not completely sure I understand it fully, but very nicely written. I really like thought experiments. I'm also intrigued by your comments about Black Holes and Hawking Radiation. This is the first time an essay has made me go back to read my own again in a new context.

Best wishes,

Antony

Anton,

If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, "It's good to be the king," is serious about our subject.

Jim

Hello Anton,

An interesting essay with an interesting problem, and if I understand the scenario correctly, and I may not, then what you are saying is that Bob has ingeniously found a way to secretly sequester part of the message directed at Charlie. For instance, if Alice is saying "Hello Charlie, how you doing today?" and Bob steals the "g today" so that Charlie receives the message "Hello Charlie, how you doin?", and Charlie replies "Hello Alice, I'm doin just fine baby.", does that mean that Alice and Charlie have experiences a non local interaction faster than the speed of light, and this due to a previous entanglement, or what? And if that's not correct, then please explain in more detail the nature of the information encoded on the communication frequency and the actual difference between what Charlie gets and what Bob gets. For your information, I have assumed that the shutter is an ideal mirror also, and that is has been shut just the once.

Zoran.

Anton,

While it is not clear to me from your experimental description exactly how your shutter is implemented (its not in any diagram I can see), it sounds to me like what you are describing is a version of a delayed choice experiment (keyword phrase: "instantaneously activated"), only while adding Bobs relativistic motion into the mix.

Any delayed choice should paradox should be excluded by special relativity given the photons own frame of reference and its time of flight within that reference (please see my paper Precognitive Quantum State: What Can We Know? if this does not make sense to you, or contact me off line and I will be happy to explain why a delayed choice is not permitted by special relativity).

Experiment after experiment have all consistently shown that delayed choice does not work (in complete agreement with my papers argument, taken directly from SR), so attempting to show that it does work mathematically is simply non-nonsensical. Something is wrong, but it will take me time to examine your experiment to find it. Every photon emitted in your experiment will wind up somewhere and thus there will be no formation loss overall, only perhaps data not yet collected due to redshift differences in relativistic motion, time dilation, or simply discarded. Photons don't just disappear (ref: first law of thermodynamics) The question then is why the difference in these two viewpoints (math vs first law of thermodynamics/numerous experiments).

If I have misunderstood something significant in my interpretation of your apparatus setup please feel free to correct me.

Dear Anton,

It's a nice essay in that, 'Information in a physical sense is that what causes the state of a physical entity to change. Viewed in this way, information is fundamental and it is a preserved quantity', is much applicable and implies that the causality of information is the transfer of matter with energy in Hamiltonian. As the nature of information is continuum, a string-matter continuum scenario is discussed to evolve a quantum information unit in matrix to resolve the information paradoxes.

With best wishes

Jayakar